1. Field of the Invention
The present invention relates to an ion implantation simulation method, and especially relates to an ion implantation simulation method for determining by simulation the impurity distribution and point defect distribution when carrying out ion implantation for a multilayer substrate used in the production of semiconductors.
2. Background Art
In semiconductor device manufacturing processes, ion implantation is widely used to form impurity regions in semiconductor substrates. In order to suitably carry out such ion implantation, there is a need to know in advance how the concentration of ions in the substrate will be distributed, in other words, to ascertain what the impurity distribution will be, and what the distribution of point defects in the substrate will be, and for this purpose, ion implantation simulations are carried out to determine, by means of the simulation, the impurity distribution and the point defect distribution.
The conventional ion implantation simulation method for determining the impurity distribution and point defect distribution in a multilayer substrate shown in FIG. 2 is carried out as follows. In FIG. 2, in a multilayer substrate composed of layers from the first to the k-th layers, k=1 is set and Q1 is set as the dose implanted into the first layer, next it is judged whether k greater than (the number of layers), and if k greater than (the number of layers), the procedure is stopped, and if kxe2x89xa6(the number of layers), a Gaussian distribution, a combined Gaussian distribution, a Pearson distribution, a dual Pearson distribution or the like is used to determine the normalized impurity distribution Ik(x) in the material of the k-th layer. If the impurity distribution Ik(x) is obtained using a Gaussian distribution, the impurity distribution Ik(x) is expressed by the following equation.                                           I            k                    ⁢                      xe2x80x83                    ⁢                      (            x            )                          =                                            C              k                                                                                            2                    ⁢                                          xe2x80x83                                        ⁢                    π                                    ⁢                                      xe2x80x83                                                              ⁢                              σ                k                                              ⁢                      xe2x80x83                    ⁢                      exp            ⁡                          [                                                -                                                            (                                              x                        -                                                  Rp                          k                                                                    )                                        2                                                                    2                  ⁢                                      xe2x80x83                                    ⁢                                      σ                    k                    2                                                              ]                                                          Eq        .                  xe2x80x83                ⁢                  (          1          )                    
In Eq. (1), Rpk is the range of ions defined for the material of the k-th layer for obtaining the impurity distribution, "sgr"k is a moment defined for the material of the k-th layer used for obtaining the impurity distribution, and x represents the coordinate in the depthwise direction. Further, Ck is determined so as to satisfy the following equations, when XSk is the transformed surface coordinate of a layer for which the material is converted into that of the k-th layer of the device,                                           ∫                          x              k                        ∞                    ⁢                                    I              k                        ⁢                          xe2x80x83                        ⁢                          (                              x                -                xs                            )                        ⁢                          xe2x80x83                        ⁢                          ⅆ              x                                      =        1                            Eq        .                  xe2x80x83                ⁢                  (          2          )                                                  xs          k                =                              x            i                    +                                    ∑                              i                =                1                                            k                -                1                                      ⁢                          xe2x80x83                        ⁢                                          (                                  1                  -                                                            Rp                      k                                                              Rp                      i                                                                      )                            ⁢              di                                                          Eq        .                  xe2x80x83                ⁢                  (          3          )                    
where, in Eq. 3, di is the width (layer thickness) of the i-th layer, and di=xi+1xe2x88x92xi. Then, the impurity distribution in the k-th layer fk(x) is determined by the following equation.                                           f            k                    ⁢                      xe2x80x83                    ⁢                      (            x            )                          =                              Q            k                    ⁢                      xe2x80x83                    ⁢                      I            k                    ⁢                      xe2x80x83                    ⁢                      (                          x              -                              xs                k                                      )                                              Eq        .                  xe2x80x83                ⁢                  (          4          )                    
Next, the point defect distribution is determined. The point defect distribution can be determined by the following equation, which corresponds to the Eq. (35) of Japanese Unexamined Patent Application, First Publication No. Hei 9-45630, previously proposed by the inventor of the present invention.                                           f            dk                    ⁢                      xe2x80x83                    ⁢                      (            x            )                          =                              F            k                    ⁢                      xe2x80x83                    ⁢                      Q            k                    ⁢                      xe2x80x83                    ⁢                      J            dk                    ⁢                      xe2x80x83                    ⁢                      (                          x              -                              (                                                      ∑                                          i                      =                      1                                                              k                      -                      1                                                        ⁢                                      xe2x80x83                                    ⁢                                                            d                      i                                        ⁡                                          [                                              1                        -                                                                              Rp                            k                                                                                Rp                            i                                                                                              ]                                                                      )                            -                              (                                                      -                                          Rp                      k                                                        +                                      Rp                    dk                                                  )                                      )                                              Eq        .                  xe2x80x83                ⁢                  (          5          )                    
Here, in Eq. (5), fdk(x) is the point defect distribution in the k-th layer, Fk is (the total amount of point defects)/(the total amount of impurities), Qk is, as mentioned above, the dose of impurities in the k-th layer, Jdk(x) is the normalized point defect distribution calculated from the moments Rpk, "sgr"dk, xcex3dk, and xcex2dk; and "sgr"dk, xcex3dk, xcex2dk are moments defined for the material of the k-th layer used for obtaining the point defect distribution, respectively representing the standard deviation, distortion and sharpness. Further, Rpdk is a range defined for the material of the k-th layer used for obtaining the point defect distribution.
The normalized point defect distribution Jdk used in Eq. (5) is defined as being calculated from the moments Rpk, "sgr"dk, xcex3dk, and xcex2dk, but this definition is unnatural because these moments are a mixture of moments in terms of the impurity distribution and moments in terms of the point defect distribution, therefore a new function referred to as Idk will be explained, in which the definition of the normalized point defect distribution is calculated from Rpdk, "sgr"dk, xcex3dk, and xcex2dk. In this way, the relationship between Jdk(x) and Idk(x) is                                           I            dk                    ⁢                      xe2x80x83                    ⁢                      (            x            )                          =                              J            dk                    ⁢                      xe2x80x83                    ⁢                      (                          x              +                              Rp                k                            -                              Rp                dk                                      )                                              Eq        .                  xe2x80x83                ⁢                  (          6          )                    
and Eq. (5) can be rewritten as follows.                                           f            dk                    ⁢                      xe2x80x83                    ⁢                      (            x            )                          =                              F            k                    ⁢                      xe2x80x83                    ⁢                      Q            k                    ⁢                      xe2x80x83                    ⁢                      I            dk                    ⁢                      xe2x80x83                    ⁢                      (                          x              -                              (                                                      ∑                                          i                      =                      1                                                              k                      -                      1                                                        ⁢                                      xe2x80x83                                    ⁢                                                            d                      i                                        ⁡                                          [                                              1                        -                                                                              Rp                            k                                                                                Rp                            i                                                                                              ]                                                                      )                                      )                                              Eq        .                  xe2x80x83                ⁢                  (          7          )                    
Here, by analogy to the impurity distribution fk(x) which is                                           ∫            xk            ∞                    ⁢                                    f              k                        ⁢                          xe2x80x83                        ⁢                          (              x              )                        ⁢                          xe2x80x83                        ⁢                          ⅆ              x                                      =                  Q          k                                    Eq        .                  xe2x80x83                ⁢                  (          8          )                    
the point defect distribution fdk(x) is defined by the following equation.                                           ∫            xk            ∞                    ⁢                                    f              dk                        ⁢                          xe2x80x83                        ⁢                          (              x              )                        ⁢                          xe2x80x83                        ⁢                          ⅆ              x                                      =                              F            k                    ⁢                      Q            k                                              Eq        .                  xe2x80x83                ⁢                  (          9          )                    
As a result, the normalized point defect distribution Idk is obtained by the following equation.                                           ∫            xk            ∞                    ⁢                                    I              dk                        ⁢                          xe2x80x83                        ⁢                          (                              x                -                                  (                                                            ∑                                              i                        =                        1                                                                    k                        -                        1                                                              ⁢                                          xe2x80x83                                        ⁢                                                                  d                        i                                            ⁡                                              [                                                  1                          -                                                                                    Rp                              k                                                                                      Rp                              i                                                                                                      ]                                                                              )                                            )                        ⁢                          xe2x80x83                        ⁢                          ⅆ              x                                      =        1                            Eq        .                  xe2x80x83                ⁢                  (          10          )                    
As a result, the point defect distribution in, for example, the second layer can be obtained by eliminating Qk using both Eqs. (8) and (9), and by setting k=2, as follows.                                           ∫            x2            ∞                    ⁢                                    f              d2                        ⁢                          xe2x80x83                        ⁢                          (              x              )                        ⁢                          xe2x80x83                        ⁢                          ⅆ              x                                      =                              F            2                    ⁢                      xe2x80x83                    ⁢                                    ∫              x2              ∞                        ⁢                                          f                2                            ⁢                              xe2x80x83                            ⁢                              (                x                )                            ⁢                              xe2x80x83                            ⁢                              ⅆ                x                                                                        Eq        .                  xe2x80x83                ⁢                  (          11          )                    
This ion implantation simulation method, proposed by the present inventor, is an analytical simulation method which is carried out using analytical equations such as Gaussian distributions, combined Gaussian distributions, and Pearson distributions.
On the other hand, the Monte Carlo ion implantation simulation method is also disclosed in the literature (Masami Hane and Masao Fukuma, xe2x80x9cIon Implantation Model Considering Crystal Structure Effectsxe2x80x9d, IEDM (1988)) as a method of ion implantation simulation. In the Monte Carlo ion implantation simulation method, as ions are implanted into the semiconductor substrate and the implanted ions advance, they are subjected to scattering by atomic nuclei, and to energy loss, and they are further subjected to energy loss by scattering by electrons present around the nuclei. Such a process is simulated for one particle at a time, and it is possible to obtain the impurity distribution after ion implantation by calculating the distribution of particles finally remaining in the semiconductor substrate.
Further, it is possible to calculate the distribution of point defects such as vacancies or interstitial atoms in a crystal after ion implantation by simulating the process by which ions expel electrons which constitute the crystal lattice.
In the Monte Carlo ion implantation simulation method, a simulation of the scattering process is made for each implanted ion, one at a time, and therefore, there is the problem that it takes a long time to obtain the results of the simulation. The present inventor disclosed an ion implantation simulation method in Japanese Unexamined Patent Application, First Publication No. Hei 9-45630, which makes it possible to obtain, in a short time, simulation results of the impurity distribution and point defect distribution by the above-mentioned analytical ion implantation simulation method.
However, in the Monte Carlo ion implantation simulation method, for ion implantation carried out in conditions in which channeling does not occur, the point defect distributions obtained for a silicon substrate when an oxide film or nitride film is present, and when no oxide film or nitride film is present, are almost the same. In contrast, in the ion implantation simulation method disclosed in the above publication, if an oxide film or nitride film is formed on the silicon substrate, the point defect distribution in the silicon substrate changes, and as a result, the point defect distribution differs from that obtained by the Monte Carlo ion implantation simulation method.
For example, as shown in FIG. 4, the impurity distribution labeled III and the point defect distribution labeled IV were obtained by the Monte Carlo ion implantation simulation method, while the ion implantation simulation method disclosed in the above publication provided the impurity distribution labeled V, which does not differ significantly from the impurity distribution III provided by the Monte Carlo ion implantation simulation method, and provided the point defect distribution labeled VI, which differs from the point defect distribution IV provided by the Monte Carlo ion implantation simulation method. This is because, when there is a nitride layer or an oxide layer on the silicon substrate, the results of the analytical simulation differ from the point defect distribution in the silicon substrate.
The present invention was made in consideration of the above points, with the objective of providing an analytical ion implantation simulation method, which can provide point defect simulation results for semiconductor substrates which are almost the same as those of the Monte Carlo ion implantation simulation method, even if there is an oxide or nitride on the semiconductor substrate.
To accomplish the above objective, the ion implantation simulation method of the present invention determines by analytical equations the impurity distribution and the point defect distribution for each layer, and simulates the point defect distribution resulting from ion implantation carried out on a multilayer substrate, by generating a point defect distribution fdk(x), related to the impurity distribution fk(x) by the following equation                                           ∫                          xs              k                        ∞                    ⁢                                    f              dk                        ⁢                          xe2x80x83                        ⁢                          (              x              )                        ⁢                          xe2x80x83                        ⁢                          ⅆ              x                                      =                              F            k                    ⁢                      xe2x80x83                    ⁢                                    ∫                              xs                k                            ∞                        ⁢                                          f                k                            ⁢                              xe2x80x83                            ⁢                              (                x                )                            ⁢                              xe2x80x83                            ⁢                              ⅆ                x                                                                        (        A        )            
(wherein fdk(x) is the actual point defect distribution of the k-th layer, fk(x) is the impurity distribution of the k-th layer, Fk is (amount of point defects)/(amount of impurities) for the k-th layer, x is the coordinate in the depthwise direction in the multilayer substrate, xsk is the transformed surface coordinate of a layer for which the material is converted into that of the k-th layer of the substrate).
The above Fk is a value calculated in advance using the equation                               F          k                =                                            ∫              0              ∞                        ⁢                                          f                d                            ⁢                              xe2x80x83                            ⁢                              (                x                )                            ⁢                              xe2x80x83                            ⁢                              ⅆ                x                                                                        ∫              0              ∞                        ⁢                          f              ⁢                              xe2x80x83                            ⁢                              (                x                )                            ⁢                              xe2x80x83                            ⁢                              ⅆ                x                                                                        (        B        )            
from the impurity distribution f(x) and the point defect distribution fd(x) calculated by Monte Carlo ion implantation simulation for conditions in which channeling does not occur, for a bare semiconductor substrate or a semiconductor substrate with a thin film on its surface of a material in which point defects do not occur.
Further, to accomplish the above mentioned objective, when ion implantation is carried out for a multilayer substrate, the method of the present invention, which determines by analytical ion implantation simulation the impurity distribution and point defect distribution for each layer, comprises a first step of determining a normalized impurity distribution, a second step of calculating the actual impurity distribution from the normalized impurity distribution, a third step of determining a reference point defect distribution, only for layers of materials for which point defects occur, and a fourth step of calculating the actual point defect distribution for ion implantation conditions which inhibit channeling, from the reference point defect distribution.
The above fourth step calculates the actual point defect distribution using the actual impurity distribution determined in the second step, and the ratio of the amount of point defects to the amount of impurities, previously calculated from the impurity distribution and point defect distribution calculated by the Monte Carlo ion implantation simulation for conditions in which channeling does not occur.
Further, the above first step is characterized in that the normalized impurity distribution is determined using one of a Gaussian distribution, a Pearson distribution, or a dual Pearson distribution.
Furthermore, the above third step is characterized in that the reference point defect distribution is determined using one of a Gaussian distribution, a Pearson distribution and a dual Pearson distribution, and normalization of the point defect distribution is not carried out.
In the present invention, it is unnecessary to distinguish layers of materials in which point defects occur from those in which point defects do not occur in order to determine the point defect distribution, because layers of materials in which point defects normally do not occur, such as oxides and nitrides, are nonetheless subject to the same degree of damage by implanted ions as layers of materials in which point defects occur, such as silicon. Therefore, in the present invention, simulations for ion implantation conditions which inhibit channeling are carried out using the same distribution as for a material in which point defects are not generated, regardless of whether the substrate has or does not have layers of material in which point defects usually do not occur, such as nitrides or oxides. dr
FIG. 1: Flowchart of an embodiment of the ion implantation simulation method of the present invention.
FIG. 2: A schematic diagram of the constitution of a multilayer substrate for ion implantation.
FIGS. 3A, 3B: Graphs explaining the determination of the impurity distribution and point defect distribution for a two layer substrate by the method of the present invention.
FIG. 4: A figure showing a comparison of the results of the simulation results for the point defect distribution by the method of the present invention, and the simulation results of the impurity distribution and point defect distribution by the Monte Carlo ion implantation simulation method.
FIG. 5: A figure showing the dual Pearson distribution used in another embodiment of the ion implantation simulation method of the present invention.